Tetrahedral symmetry in Zr nuclei: Calculations of low-energy excitations with Gogny interaction

Abstract

We report on the results of the calculations of the low energy excitation patterns for three Zirconium isotopes, viz. ${}^{80}$Zr${}_{40}$, ${}^{96}$Zr${}_{56}$ and ${}^{110}$Zr${}_{70}$, reported by other authors to be doubly-magic tetrahedral nuclei (with tetrahedral magic numbers $Z$=40 and $N$=40, 56 and 70). We employ the realistic Gogny effective interactions using three variants of their parametrisation and the particle-number, parity and the angular-momentum projection techniques. We confirm quantitatively that the resulting spectra directly follow the pattern expected from the group theory considerations for the tetrahedral symmetric quantum objects. We also find out that, for all the nuclei studied, the correlation energy obtained after the angular momentum projection is very large for the tetrahedral deformation as well as other octupole deformations. The lowering of the energies of the resulting configurations is considerable, i.e. by about 10 MeV or even more, once again confirming the significance of the angular-momentum projections techniques in the mean-field nuclear structure calculations.

References in corpus (5)

• Tetrahedral correlations in ${}^{80}$Zr and ${}^{98}$Zr
• Nuclei with Tetrahedral Symmetry
• Nuclear tetrahedral states and high-spin states studied using quantum number projection method
• The suggested presence of the tetrahedral-symmetry in the ground-state configuration of the ${}^{96}$Zr nucleus
• Efficient Method for Quantum Number Projection and Its Application to Tetrahedral Nuclear States

Cited by in corpus (6)

• Ground state octupole correlation energies with effective forces
• Anatomy of octupole correlations in ${}^{96}$Zr with a symmetry-restored multidimensionally-constrained covariant density functional theory
• Oxygen-16 Spectrum from Tetrahedral Vibrations and their Rotational Excitations
• $g$-matrix folding-model approach to reaction cross sections for scattering of Ca isotopes on a C target
• Enlarged deformation region in neutron-rich Zr isotopes by the second intruder orbit
• Tetrahedral shape and Lambda impurity effect in ${}^{80}$Zr with a multidimensionally constrained relativistic Hartree-Bogoliubov model